Related papers: Surface Operators and Separation of Variables
We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary…
We examine dualities of two dimensional conformal field theories by applying the methods developed in previous works. We first derive the duality between $SL(2|1)_k/(SL(2)_k \otimes U(1))$ coset and Witten's cigar model or sine-Liouville…
Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to…
We prove that the cigar conformal field theory is dual to the Sine-Liouville model, as conjectured originally by Fateev, Zamolodchikov and Zamolodchikov. Since both models possess the same chiral algebra, our task is to show that…
We study half-BPS surface operators in N=2 supersymmetric QCD in four dimensions with gauge group SU(2) and four fundamental flavours. We compute the twisted chiral superpotential that describes the effective theory on the surface operator…
Recently Alday and Tachikawa proposed a relation between conformal blocks in a two-dimensional theory with affine sl(2) symmetry and instanton partition functions in four-dimensional conformal N=2 SU(2) quiver gauge theories in the presence…
We derive a relation between correlation functions of supergroup WZNW models and conformal field theories with extended superconformal symmetry. The supergroups considered have a bosonic subgroup of the form SL(2) x A for some Lie group A.…
We investigate 1/2 BPS conformal surface operators in the Klebanov-Witten theory. These surface operators preserve certain parts of the conformal symmetry and R-symmetry as well as half of the supersymmetry. We propose the gravity dual of…
Higher dimensional Euclidean Liouville conformal field theories (LCFTs) consist of a log-correlated real scalar field with a background charge and an exponential potential. We analyse the LCFT on a four-dimensional manifold with a boundary.…
We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We…
The 6d $\mathcal{N}=(2,0)$ theory has natural surface operator observables, which are akin in many ways to Wilson loops in gauge theories. We propose a definition of a "locally BPS" surface operator and study its conformal anomalies, the…
We study half-BPS surface operators in four dimensional N=2 SU(N) gauge theories, and analyze their low-energy effective action on the four dimensional Coulomb branch using equivariant localization. We also study surface operators as…
We present our recent studies on the dynamics of boundary N=2 Liouville theory. We use the representation theory of N=2 superconformal algebra and the method of modular bootstrap to derive three classes of boundary states of the N=2…
We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and anti-chiral sectors in the 2d RCFT. The…
We compute the correlation functions of irregular Gaiotto states appearing in the colliding limit of the Liouville theory by using "regularizing" conformal transformations mapping the irregular (coherent) states to regular vertex operators…
We study brane configurations which correspond to field theories in four dimension with N=2 and N=1 supersymmetry. In particular we discuss brane motions that translate to Seiberg's duality in N=1 models recently studied by Elitzur, Giveon…
Surface operators in four-dimensional gauge theories are two-dimensional defects, serving as natural generalizations of Wilson lines and 't Hooft line operators. They act as ideal probes for exploring the non-perturbative structure of the…
We propose new strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten's cigar model described by the $\mathfrak{sl}(2)/\mathfrak{u}(1)$ coset and…
Surface operators in gauge theory are analogous to Wilson and 't Hooft line operators except that they are supported on a two-dimensional surface rather than a one-dimensional curve. In a previous paper, we constructed a certain class of…
We study rigid surface operators in the $N=4$ supersymmetric Yang-Mills theories with gauge groups $SO(n)$ and $Sp(2n)$. Using maps $X_S$ and $Y_S$ between these two theories, Wyllard made explicit proposals for how the $S$-duality map…